Integration by substitution, but I cannot see how

Question

I am trying to find an indefinite integral. The question suggests that it can be solved with integration by substitution, but I cannot see how. Multiplying out the brackets and integrating gives an eight-order result. Can anyone help here?

$$ \int \left(x+4\right)\left(\frac{1}{3}x+8\right)^6\:dx $$

Answer 1

Isn't it natural to set $u=x/3+8$ ?

Then

$$\int \left(x+4\right)\left(\frac{1}{3}x+8\right)^6\:dx=3\int \left(3u-20\right)u^6\:du$$

which should be easy. (By the way, in all cases integrating a polynomial is easy.)